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Chapter 14 Waves and Sound
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14-1 Types of Waves A wave is a disturbance that propagates from one place to another. The easiest type of wave to visualize is a transverse wave, where the displacement of the medium is perpendicular to the direction of motion of the wave.
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14-1 Types of Waves In a longitudinal wave, the displacement is along the direction of wave motion.
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14-1 Types of Waves Water waves are a combination of transverse and longitudinal waves.
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14-1 Types of Waves Wavelength λ: distance over which wave repeats
Period T: time for one wavelength to pass a given point Frequency f: Speed of a wave:
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14-2 Waves on a String The speed of a wave is determined by the properties of the material through which it propagates. For a string, the wave speed is determined by: the tension in the string, and the mass of the string. As the tension in the string increases, the speed of waves on the string increases as well.
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14-2 Waves on a String The total mass of the string depends on how long it is; what makes a difference in the speed is the mass per unit length. We expect that a larger mass per unit length results in a slower wave speed.
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14-2 Waves on a String As we can see, the speed increases when the force increases, and decreases when the mass increases.
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14-2 Waves on a String When a wave reaches the end of a string, it will be reflected. If the end is fixed, the reflected wave will be inverted:
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14-2 Waves on a String If the end of the string is free to move transversely, the wave will be reflected without inversion.
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14-3 Harmonic Wave Functions
Since the wave has the same pattern at x + λ as it does at x, the wave must be of the form Also, as the wave propagates in time, the peak moves as
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14-3 Harmonic Wave Functions
Combining yields the full wave equation:
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14-4 Sound Waves Sound waves are longitudinal waves, similar to the waves on a Slinky: Here, the wave is a series of compressions and stretches.
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14-4 Sound Waves In a sound wave, the density and pressure of the air (or other medium carrying the sound) are the quantities that oscillate.
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14-4 Sound Waves The speed of sound is different in different materials; in general, the denser the material, the faster sound travels through it.
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14-4 Sound Waves Sound waves can have any frequency; the human ear can hear sounds between about 20 Hz and 20,000 Hz. Sounds with frequencies greater than 20,000 Hz are called ultrasonic; sounds with frequencies less than 20 Hz are called infrasonic. Ultrasonic waves are familiar from medical applications; elephants and whales communicate, in part, by infrasonic waves.
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14-5 Sound Intensity The intensity of a sound is the amount of energy that passes through a given area in a given time.
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14-5 Sound Intensity Expressed in terms of power,
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14-5 Sound Intensity Sound intensity from a point source will decrease as the square of the distance.
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14-5 Sound Intensity Bats can use this decrease in sound intensity to locate small objects in the dark.
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14-5 Sound Intensity When you listen to a variety of sounds, a sound that seems twice as loud as another is ten times more intense. Therefore, we use a logarithmic scale to define intensity values. Here, I0 is the faintest sound that can be heard:
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14-5 Sound Intensity The quantity β is called a bel; a more common unit is the decibel, dB, which is a tenth of a bel. The intensity of a sound doubles with each increase in intensity level of 10 dB.
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14-6 The Doppler Effect The Doppler effect is the change in pitch of a sound when the source and observer are moving with respect to each other. When an observer moves toward a source, the wave speed appears to be higher, and the frequency appears to be higher as well.
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14-6 The Doppler Effect The new frequency is:
If the observer were moving away from the source, only the sign of the observer’s speed would change:
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14-6 The Doppler Effect To summarize:
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14-6 The Doppler Effect The Doppler effect from a moving source can be analyzed similarly; now it is the wavelength that appears to change:
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14-6 The Doppler Effect We find:
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14-6 The Doppler Effect Here is a comparison of the Doppler shifts for a moving source and a moving observer. The two are similar for low speeds but then diverge. If the source moves faster then the speed of sound, a sonic boom is created.
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14-6 The Doppler Effect Combining results gives us the case where both observer and source are moving: The Doppler effect has many practical applications: weather radar, speed radar, medical diagnostics, astronomical measurements.
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14-6 The Doppler Effect At left, a Doppler radar shows the hook echo characteristic of tornado formation. At right, a medical technician is using a Doppler blood flow meter.
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